Hölder continuity for Trudinger's equation in measure spaces

Tuomo Kuusi; Rojbin Laleoglu; Juhana Siljander; José Miguel Urbano

doi:10.1007/s00526-011-0456-1

Hölder continuity for Trudinger's equation in measure spaces

Tuomo Kuusi^*, Rojbin Laleoglu, Juhana Siljander, José Miguel Urbano

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

University of Coimbra

Research output: Contribution to journal › Article › Scientific › peer-review

26 Citations (Scopus)

Abstract

We complete the study of the regularity for Trudinger's equation by proving that weak solutions are Hölder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling.

Original language	English
Pages (from-to)	193-229
Number of pages	37
Journal	Calculus of Variations and Partial Differential Equations
Volume	45
Issue number	1-2
DOIs	https://doi.org/10.1007/s00526-011-0456-1
Publication status	Published - Sept 2012
MoE publication type	A1 Journal article-refereed

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title = "H{\"o}lder continuity for Trudinger's equation in measure spaces",

abstract = "We complete the study of the regularity for Trudinger's equation by proving that weak solutions are H{\"o}lder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincar{\'e} inequality. The proof uses the Harnack inequality and intrinsic scaling.",

author = "Tuomo Kuusi and Rojbin Laleoglu and Juhana Siljander and Urbano, {Jos{\'e} Miguel}",

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AU - Kuusi, Tuomo

AU - Laleoglu, Rojbin

AU - Siljander, Juhana

AU - Urbano, José Miguel

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Y1 - 2012/9

N2 - We complete the study of the regularity for Trudinger's equation by proving that weak solutions are Hölder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling.

AB - We complete the study of the regularity for Trudinger's equation by proving that weak solutions are Hölder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling.

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DO - 10.1007/s00526-011-0456-1

M3 - Article

AN - SCOPUS:84865630591

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EP - 229

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 1-2

ER -

Hölder continuity for Trudinger's equation in measure spaces

Abstract

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